**Matrix: Janna/Serena**

Description: gas resevoir simulation for CO2 sequestration

(undirected graph drawing) |

Matrix properties | |

number of rows | 1,391,349 |

number of columns | 1,391,349 |

nonzeros | 64,131,971 |

structural full rank? | yes |

structural rank | 1,391,349 |

# of blocks from dmperm | 9,229 |

# strongly connected comp. | 9,229 |

explicit zero entries | 399,730 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | yes |

positive definite? | yes |

author | C. Janna, M. Ferronato |

editor | T. Davis |

date | 2011 |

kind | structural problem |

2D/3D problem? | yes |

Notes:

Authors: Carlo Janna and Massimiliano Ferronato Symmetric Positive Definite Matrix # equations: 1,391,349 # non-zeroes: 64,531,701 Problem description: structural problem The matrix Serena is obtained from a structural problem discretizing a gas reservoir with tetrahedral Finite Elements. The medium is strongly heterogeneous and characterized by a complex geometry consisting of alternating sequences of thin clay and sand layers. Some further information may be found in the paper: M. Ferronato, G. Gambolati, C. Janna, P. Teatini. "Geomechanical issues of anthropogenic CO2 sequestration in exploited gas fields", Energy Conversion and Management, 51, pp. 1918-1928, 2010.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 7,502,311,154 |

Cholesky flop count | 2.2e+14 |

nnz(L+U), no partial pivoting, with AMD | 15,003,230,959 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 11,091,348,271 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 19,624,945,409 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 399730 explicit zero entries.
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*For a description of the statistics displayed above,
click here.
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*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*